Statistical mechanics and Gibbs measures
MATH-486 / 5 credits
Teacher:
Language: English
Remark: Pas donné en 2022-23 - Donné en alternance une année sur deux
Summary
This course provides a rigorous introduction to the ideas, methods and results of classical statistical mechanics, with an emphasis on presenting the central tools for the probabilistic description of infinite lattice systems.
Content
The goals of this course are to present
- the probabilistic description of large systems with interacting components,
- the mathematical description of phase transitions occuring in certain discrete models (Curie-Weiss, Ising model, long-range models, etc.)
- the general theory of infinite-volume Gibbs measures (the so-called Dobrushin-Lanford-Ruelle approach)
If times permits, and depending on the interest of the participants, we consider the peculiar properties of certain models with an underlying continuous symmetry (Gaussian free field, Mermin-Wagner Theorem for O(n) models).
This course is companion to the course ``lattice models'', where discrete models
are also considered, but with an emphasis on different aspects.
The lectures will be largely based on the book Statistical mechanics of lattice systems; a concrete mathematical introduction, by S. Friedli and Y. Velenik (Cambridge University Press, 2017)
Keywords
statistical mechanics, phase transitions, Gibbs measures, entropy, Ising model, Gaussian Free Field
Learning Prerequisites
Required courses
- Analyse 1et 2
- Théorie de la Mesure
- Probabilités
Assessment methods
Examen oral.
Dans le cas de l’art. 3 al. 5 du Règlement de section, l’enseignant décide de la forme de l’examen qu’il communique aux étudiants concernés.
Resources
Bibliography
Statistical mechanics of lattice systems; a concrete mathematical introduction, by S. Friedli and Y. Velenik (Cambridge University Press, 2017)
Gibbs Measures and Phase Transitions, by H.-O. Georgii (De Gruyter Studies in Mathematics Vol. 9. Berlin: de Gruyter 1988)
Ressources en bibliothèque
In the programs
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Statistical mechanics and Gibbs measures
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Statistical mechanics and Gibbs measures
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Statistical mechanics and Gibbs measures
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Statistical mechanics and Gibbs measures
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Statistical mechanics and Gibbs measures
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Statistical mechanics and Gibbs measures
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Semester: Spring
- Exam form: Oral (summer session)
- Subject examined: Statistical mechanics and Gibbs measures
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
Reference week
| Mo | Tu | We | Th | Fr | |
| 8-9 | |||||
| 9-10 | |||||
| 10-11 | |||||
| 11-12 | |||||
| 12-13 | |||||
| 13-14 | |||||
| 14-15 | |||||
| 15-16 | |||||
| 16-17 | |||||
| 17-18 | |||||
| 18-19 | |||||
| 19-20 | |||||
| 20-21 | |||||
| 21-22 |
Légendes:
Lecture
Exercise, TP
Project, other